The present invention relates to a new and distinct variety of white flat peach tree, Prunus persica L. Batsch, which has been given the variety denomination ‘FLATOP’. This new tree produces fruit with a long shelf life without alteration both on the tree after growth completion and after harvesting, very good eating quality, clingstone or semi-clingstone white flesh fruit for fresh market in August in the Pyrénées-Orientales department, France. Contrast is made to ‘Flatpretty’ (Plant Pat. No. 21,389), a white flat peach tree and to ‘ASFPBF0796’ (U.S. Plant Pat. No 22,495), a white flat peach tree, and to its parents, ‘Nectarmagie’ (U.S. Plant Pat. No. 17,579) white nectarine tree and ‘ASFPBF0492’ (U.S. Plant Pat. No. 21,143) white flat peach tree, for reliable description. ‘FLATOP’ is a promising candidate for commercial success in that it has very attractive fruits with very long shelf life without alteration before after harvesting.